
where \(\underline{{\beta }}\)  is a vector of unknown parameters, and \(\underline{\epsilon }\)  is the disturbance term. With an unknown link function, this model avoids the curse of dimensionality in many nonparametric models and reduces the risk of model misspecification, while maintaining relative ease of interpretation [1]}, [2]}.
Various approaches have been proposed to estimate the SIM, e.g., average derivative estimation [3]}, nonlinear least squares [4]}, and profile least-squares [5]}. All of these methods require correct specification of the covariates.
However, this knowledge is often unavailable in practice, especially when there are many covariates, so researchers are exposed to a potentially large degree of model uncertainty with respect to which covariates should be included in the model.
